1. Field of the Invention
The present invention relates to an optical device for vertically positioning a sextant to minimize the "tilt error" which occurs in the measured angle of altitude whenever the sextant is not held orthogonal to the horizon. More particularly, the invention is directed to an optical device which provides in the sextant's viewing area a secondary horizon which will align with the direct horizon only when the sextant is in a vertical orientation. The optical device is positioned along the line of sight and preferably, but not necessarily between the sextant's horizon mirror and eyepiece, is capable of being calibrated, and can be pivoted out of the line of sight when the sextant's user is initially locating the celestial body whose altitude is to be measured.
2. Description of the Prior Art
It is well-known that a marine sextant is used for measuring the angular altitude of celestial bodies above the sea horizon. By accurately measuring the angular altitude of a given celestial body at a given time, a skilled navigator can determine a line of position. With two or more such lines, the navigator can calculate his position. It is important that the angle be measured as accurately as possible since an error of only one minute of arc will result in a position error of at least one nautical mile.
As will be described below, any misalignment in the elements of a sextant will lead to errors in the sextant's reading. It is therefore important that a sextant be properly calibrated each time it is used. Sextants typically provide a means for such calibration. Even if a sextant is perfectly calibrated, however, the sextant's reading will include a "tilt error" unless the sextant is perfectly orthogonal to the horizon. Since readings from a sextant normally are taken from a rolling ship, it is exceedingly difficult to align the sextant vertically. As will be explained below, applicant has invented an optical device designed to facilitate the vertical positioning of a sextant.
In order to understand and appreciate the present invention, it is necessary to briefly explain the use and operation of a sextant, the causes of errors in a sextant's reading, and present methods of correcting or attempting to correct those errors.
A typical sextant, referred to generally as 8, is shown in FIG. 1. The sextant includes a frame 10, a handle 14 fixed to frame 10, and an index arm 16 pivotably connected to frame 10. A telescope or eyepiece 18 is connected to frame 10 and is aligned with a horizon mirror 20 which is also fixed to the frame. The horizon mirror 20 is constructed so that light from the horizon may come directly through all or a portion of the mirror, enabling a navigator to view through the eyepiece 18 the horizon directly in front of him. The horizon mirror also is constructed so that all or a portion of the mirror will reflect light from its surface toward the eyepiece 18. The sextant also includes an index mirror 22 fixed to the index arm 16. The index mirror is reflective only, and in combination with the horizon mirror 20 will provide a navigator with a reflected view of a celestial body in the eyepiece 18. When the index mirror 22 and horizon mirror 20 are parallel to one another, the sextant should read 0.degree. on the limb 12 at arc 24. The index mirror 22 is rotatable relative to the horizon mirror 20, and that rotation can be effected by micrometer dial 26.
When using a sextant, a navigator observes both the horizon H through the horizon mirror and a celestial body C whose image is double reflected, first from the index mirror 22 to the horizon mirror 20, and second from the horizon mirror 20 to the eyepiece 18. When the sextant is vertical and the rays of the horizon H and celestial body C are aligned, the angulation read from the arc 24 and the micrometer dial 26 is directly related to the altitude of the celestial body C. A more detailed explanation of the use of a sextant is described in these books: F. D. Wright, Celestial Navigation, (Cornell Maritime Press, 4th Printing 1980); N. Bowditch, American Practical Navigator, (GPO 1966).
For a sextant to give a proper reading, it is important that both the index mirror and the horizon mirror be perpendicular to the frame of the sextant. It is also important that the index mirror and horizon mirror be parallel to each other when the sextant is placed at the zero setting. in view of the importance of these relationships, most sextants include mechanical means for adjusting and calibrating the perpendicularity and parallelism of the index and horizon mirrors. A good navigator calibrates the placement of the index and horizon mirror before taking any readings, and the methods of accomplishing this calibration are well-known. For example, these steps are described in American Practical Navigator, pp. 412-415, supra.
A perfectly calibrated sextant will still give erroneous measurements unless the plane of the body of the sextant is precisely vertical when a reading is taken. If it is not, the measured angle of altitude will be greater than the actual angle of altitude, regardless of which direction the sextant is tilted. As is known in the art, the altitude of a celestial body is its vertical angle above the horizon. It is apparent that the angular distance from the celestial body to any point on the horizon other than the point vertically below the body is greater than its actual altitude. The difference in the actual and measured altitude is a "tilt error" which can lead to significant errors in a sextant reading. First, the degree of tilt cannot be measured on a rolling ship, and generally the sextant's user is not aware of the existence or nonexistence of tilt. Tilt error increases as the angle of tilt increases and is believed to increase with an increase in the altitude of the celestial body being observed, at least until that altitude reaches 45.degree.. Some persons believe that the tilt error is maximum for a celestial body having an altitude of 45.degree. and decreases with larger and smaller altitudes. It is generally agreed, however, that tilt error can lead to significant navigational errors. Furthermore, the tilt error will not self correct by taking the average of several readings since each tilt error, regardless of the direction of tilt, will result in an increased reading.
Although the problems associated with tilt error have been recognized for many years, the only currently applied method of attempting to vertically position a sextant is a complicated procedure called dipping or rocking. The process is illustrated in FIG. 2. Once a navigator simultaneously positions the image of the celestial body and the horizon in the sextant's viewing area, he must then orient the sextant in a vertical position and place the image of the celestial body on the observed horizon by manipulating the sextant's micrometer drum. According to the dipping procedure, the navigator must rock the sextant gently with his right hand until he sees the celestial body's image moving on an arc to the left and then to the right, as shown in FIG. 2. The object of the dipping process is to turn the micrometer drum so that the image of the celestial body is perfectly tangent to the horizon at the lowest point of its arc. If the navigator can accomplish that objective and immediately "mark" the time when he is successful, then at least theoretically the resultant reading is one taken when the sextant is vertical. This procedure is described in American Practical Navigator, supra, p. 402 and Celestial Navigation, supra, pp. 18-19.
It has been the inventor's experience that many neophyte navigators, and indeed some more seasoned navigators, are inept at the rather awkward procedure of dipping. It is therefore believed that tilt error is fairly prevalent and more consequential than is generally thought. The inventor has also concluded that the degree of tilt error depends upon how the sextant is rocked. Many navigators rock the sextant about a horizontal axis, and others rock the sextant about a line drawn from the sextant to the star. It is the inventor's conclusion that the tilt error is greater when the sextant is rocked about a horizontal axis. In either circumstance, however, the error is substantial. The inventor has calculated that tilting a sextant 5.degree. out of vertical when measuring a star at a 45.degree. altitude can result in a 13 mile error in the line of position, if the sextant is being rocked about a horizontal axis, and a 6.6 mile error, if the sextant is rocked about a line drawn from the sextant to the star. The author of an authoritative text on the subject of celestial navigation has similarly concluded that a 10.degree. tilt out of vertical would cause a 26 minute (or 26 nautical mile) error for a celestial body having an altitude of 45.degree.. Celestial Navigation, supra, p. 19. Since two or more lines of position must be taken to determine position, the resultant position error can be substantial.